According to Robert Twigger in Angry White Pyjamas, because you washing them would dissipate the ki (mystic energy), so by the time you reached that level belts were already naturally black
August 18, 2008 at 1:54 am (Japan and the Olympics, Japan FAQs and SAQs, Japanese celebrities, Japanese comics (manga), Japanese martial arts, Japanese names, Judo)
Tags: Ryoko Tani, Urayasu tekkin kazoku (super radical gag family)
Being the nickname for the judoka Ryoko Tani (谷亮子 Tani Ryouko). According to Wikipedia (where else?), it comes from the name of a popular series of manga about judo.
The next question then is, why is she soooooooooooooo popular? That includes the ultimate compliment for any celebrity, starring more than once in the manga Urayasu Tekkin Kazoku (“English” title Super Radical Gag Family)